In recent years, the Metis prover based on ordered paramodulation and model elimination has replaced the earlier built-in methods for general-purpose proof automation in HOL4 and Isabelle/HOL. In the annual CASC competition, the leanCoP system based on con-nection tableaux has however performed better than Metis. In this paper we show how the leanCoP’s core algorithm can be imple-mented inside HOL Light. leanCoP’s flagship feature, namely its minimalistic core, results in a very simple proof system. This plays a crucial role in extending the MESON proof reconstruction mech-anism to connection tableaux proofs, providing an implementation of leanCoP that certifies its proofs. We discuss the differences be-tween our direct implementation using an explicit Prolog stack, to the continuation passing implementation of MESON present in HOL Light and compare their performance on all core HOL Light goals. The resulting prover can be also used as a general purpose TPTP prover. We compare its performance against the resolution based Metis on TPTP and other interesting datasets.

Abstract We describe a system offering deduction (over a fixed but flexible background theory) as a service, provided to a client via a network connection. The deduction server maintains the (potentially) large background knowledge base in a form that makes processing of individual conjectures and queries easy and avoids most of the overhead of reading and analyzing large background theories for each individual job. The client connects to the server, can update the background theory by adding and removing client-side or server-side axiom sets, and ask the server to solve proof problems on its behalf. This offers several benefits: Preprocessing costs can be amortized over multiple proof attempts. The user can be isolated from the complexities of a locally installed ATP system (and indeed locally maintained knowledge bases). Finally, the deduction server can easily offer true strategy parallelism even with sequential back-end theorem provers. This paper describes the architecture, the communication protocol, and the implementation of a deduction server based on E. First experimental results demonstrate the feasibility of the technology and the performance benefits possible with this approach.